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The shortest focal length f and smallest chromatic aberration constant C c of an objective lens is directly proportional to the square root of the (corrected) accelerating voltage V r and inversely proportional to the maximum magnetic field strength H p in the parallel part of the pole piece gap For given values of V r and H p , both f and C c fall monotonically with the relative pole-piece separation S/D , although the reduction is insignificant for S/D >2. For each lens geometry there exists an optimum set of lens dimensions
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George W. Liebmann (1952) studied this question.
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